The beginning of the adhan

Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) states: When Allah Almighty intended to teach His Messenger the method of the adhan, Sayyiduna Jibril (peace be upon him) brought the Prophet (peace and blessings be upon him) an animal called al-Buraq. The Prophet (peace and blessings be upon him) went to mount it, but it became restive. Sayyiduna Jibril said to it, "Be calm! By Allah, no servant more honoured in the sight of Allah Almighty than Sayyiduna Muhammad (peace and blessings be upon him) has ever ridden you." The narrator states: So the Prophet (peace and blessings be upon him) mounted it until he reached the veil that is next to the Most Merciful. While he was there, an angel came out from the veil. The Prophet (peace and blessings be upon him) asked, "O Jibril, who is this?" He replied, "By the One who sent you with the truth, in terms of position I am the nearest of creation, yet since I was created I have never seen this angel before this hour of mine." The angel said, "Allahu akbar, Allahu akbar (Allah is the Greatest, Allah is the Greatest)." Then it was said to him from behind the veil, "My servant has spoken the truth; I am the Greatest, I am the Greatest." Then the angel recited, "I bear witness that there is no god besides Allah Almighty." It was said from behind the veil, "My servant has spoken the truth; there is no god besides Me." The angel said, "I bear witness that Sayyiduna Muhammad (peace and blessings be upon him) is the Messenger of Allah." It was said from behind the veil, "My servant has spoken the truth; I sent Sayyiduna Muhammad (peace and blessings be upon him)." The angel said, "Come to prayer, come to success, the prayer has been established." Then he said, "Allahu akbar, Allahu akbar." It was said from behind the veil, "My servant has spoken the truth; I am the Greatest, I am the Greatest." Then the angel recited, "La ilaha illallah (there is no god but Allah)." It was said from behind the veil, "My servant has spoken the truth; there is no god besides Me." The narrator states: Then the angel took hold of the hand of Sayyiduna Muhammad (peace and blessings be upon him) and put him forward, and the Prophet (peace and blessings be upon him) led all the inhabitants of the heavens in prayer, among whom were Sayyiduna Adam (peace be upon him) and Sayyiduna Nuh (peace be upon him). Imam Abu Ja'far Muhammad bin Ali (that is, Imam al-Baqir) says: On that day Allah Almighty perfected the honour of Sayyiduna Muhammad (peace and blessings be upon him) over all the inhabitants of the heavens and the earth.
Imam al-Bazzar recorded this narration. Its chain contains a narrator, Ziyad bin al-Mundhir, who is agreed upon to be da'if (weak).

Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) states: When the Prophet (peace and blessings be upon him) was taken up to the heavens, Allah Almighty revealed to him the method of the adhan. He came down with it, and Sayyiduna Jibril (peace be upon him) taught it to him.
Imam al-Tabarani recorded this narration in al-Mu'jam al-Awsat. Its chain contains a narrator, Talhah bin Zayd, who has been accused of fabricating hadith.

Sayyiduna Buraydah (may Allah be pleased with him) states: A man from the Ansar passed by the Prophet (peace and blessings be upon him) while he (the man) was grieved. The man used to prepare food, and people used to gather at his place. He entered his mosque and began to pray. While he was in that state, he dozed off, and someone came to him in his sleep and said, "I know what you are grieved about." Then the narrator related the whole story of the adhan. The Prophet (peace and blessings be upon him) said, "Abu Bakr has been told the like of what you have been told. Tell Bilal to give the adhan in this way."
Imam al-Tabarani recorded this narration in al-Mu'jam al-Awsat. Its chain contains a narrator about whom there has been criticism, but he is thiqah (trustworthy).